I am running a two-level analysis using 4 latent variables. I have already got a good fit model to data but I'd like to test if the alternative models are giving a better/worse fit. I am not sure how to run this. Here is what the model looks like:

A --> B --> C --> D where B is used in both within and between groups, A is the within variable and C and D are between variables.

I wonder if I can test a model by restricitng some or all mediating paths so the models are:

1) A --> C --> D 2) A --> D

Also, I'd like to know if I can run chi-square difference tests from imposting these restrictions.